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The Unscented Kalman filter (UKF) is the popular approach to estimate the recursive parameter of nonlinear dynamical system corrupted with Gaussian and white noises. Also, it has been applied to train the weights of the multi-layered neural network (MNN) models. The Group method of data handling (GMDH)-type neural network is one of the most widely used neural networks which has high capacity in modeling of the complex data. In many researches, different approaches are used in training of neural networks in terms of associated weights or coefficients, such as singular value decomposition, and genetic algorithms. In this paper, the unscented Kalman filter is used to train the parameters of GMDH-type neural network when the experimental data are deterministic. The effectiveness of GMDH-type neural network with UKF algorithm is demonstrated by the modeling of the using a table of the multi input-single output experimental data. The simulation result shows that the UKF-based GMDH algorithm perform well in modeling of nonlinear systems in comparison with the results of using traditional GMDH-type neural network and is more robust against the model and measurement uncertainty.

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The early success in the 1960s of the Kalman filter in aerospace applications led to attempts to apply it to more common industrial applications in the 1970s. However, these attempts quickly made it clear that a serious mismatch existed between the underlying assumptions of Kalman filters and industrial state estimation problems. Accurate system models and statistical nature of the noise processes are not as readily available for industrial problems. In this paper, a novel method of combining two nonlinear unscented Kalman filter and "H" _∞ unscented Kalman filter is presented so that the results are a compromise between in addition of more reliability compared to that of two other filters. One characteristic of this filter is no need to linearize of the nonlinear problems and gives more suitable results than other two filters with non-Gaussian noise. Investigations show, when in a part of estimating the UKF is best and in the other part the UHF, the hybrid filter can give better results with present a compromise estimation. The variance analysis indicated that the filter is robust to statistical noise nature and a proper response can be found by changing its variable. Validation of results is performed by simulation of two nonlinear problems, free falling and inverted pendulum in mechanical engineering.